Simplify (-2(v^-1)^2)/(-5v)

$\frac{- 2 {(v^{- 1})}^{2}}{- 5 v}$

Step 1

Simplify the numerator.

Multiply the exponents in ${(v^{- 1})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{- 2 v^{- 1 \cdot 2}}{- 5 v}$

Multiply $- 1$ by $2$ .

$\frac{- 2 v^{- 2}}{- 5 v}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 2 \frac{1}{v^{2}}}{- 5 v}$

Step 2

Combine fractions.

Combine $- 2$ and $\frac{1}{v^{2}}$ .

$\frac{\frac{- 2}{v^{2}}}{- 5 v}$

Move the negative in front of the fraction.

$\frac{- \frac{2}{v^{2}}}{- 5 v}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- \frac{2}{v^{2}} \cdot \frac{1}{- 5 v}$

Step 4

Move the negative in front of the fraction.

$- \frac{2}{v^{2}} (- \frac{1}{(5) v})$

Step 5

Multiply $- \frac{2}{v^{2}} (- \frac{1}{5 v})$ .

Multiply $- 1$ by $- 1$ .

$1 \frac{2}{v^{2}} \frac{1}{5 v}$

Multiply $\frac{2}{v^{2}}$ by $1$ .

$\frac{2}{v^{2}} \cdot \frac{1}{5 v}$

Multiply $\frac{2}{v^{2}}$ by $\frac{1}{5 v}$ .

$\frac{2}{v^{2} (5 v)}$

Multiply $v^{2}$ by $v$ by adding the exponents.

Move $v$ .

$\frac{2}{v \cdot v^{2} \cdot 5}$

Multiply $v$ by $v^{2}$ .

Raise $v$ to the power of $1$ .

$\frac{2}{v^{1} v^{2} \cdot 5}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2}{v^{1 + 2} \cdot 5}$

Add $1$ and $2$ .

$\frac{2}{v^{3} \cdot 5}$

Step 6

Move $5$ to the left of $v^{3}$ .

$\frac{2}{5 v^{3}}$